# PCA
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## The goal


Questions to [David Rotermund](mailto:davrot@uni-bremen.de)

```python
import numpy as np
import matplotlib.pyplot as plt

rng = np.random.default_rng(1)

a_x = rng.normal(0.0, 1.0, size=(5000))[:, np.newaxis]
a_y = rng.normal(0.0, 1.0, size=(5000))[:, np.newaxis] ** 3
data_a = np.concatenate((a_x, a_y), axis=1)

b_x = rng.normal(0.0, 1.0, size=(5000))[:, np.newaxis] ** 3
b_y = rng.normal(0.0, 1.0, size=(5000))[:, np.newaxis]
data_b = np.concatenate((b_x, b_y), axis=1)

data = np.concatenate((data_a, data_b), axis=0)

angle = -0.3

roation_matrix = np.array(
    [[np.cos(angle), -np.sin(angle)], [np.sin(angle), np.cos(angle)]]
)
data_r = data @ roation_matrix

plt.plot(data[:, 0], data[:, 1], "b.")
plt.plot(data_r[:, 0], data_r[:, 1], "r.")
```

![image0](image0.png)